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A073403
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Coefficient triangle of polynomials (falling powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073404.
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4
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1, 12, 36, 120, 888, 1536, 1152, 15168, 62592, 80448, 10944, 222336, 1600704, 4813056, 5068800, 103680, 2992896, 32811264, 169917696, 413351424, 375598080, 981504, 38112768, 587976192, 4592982528
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The row polynomials are p(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..
The k-th convolution of U0(n) := A002605(n), n>= 0, ((2,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073387(n+k,k) = 2*(p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*U0(n))/(k!*12^k), k=1,2,..., where the companion polynomials q(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073404(k,m).
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LINKS
| W. Lang First 7 rows.
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FORMULA
| Recursion for row polynomials defined in the comments: see A073405.
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EXAMPLE
| k=2: U2(n)=(2*(36+12*n)*(n+1)*U0(n+1)+2*(36+12*n)*(n+2)*U0(n))/(2!*12^2), cf. A073389.
1; 12,36; 120,888,1536; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
| Cf. A002605, A073387, A073404.
Sequence in context: A060621 A058880 A055551 * A064518 A135178 A085331
Adjacent sequences: A073400 A073401 A073402 * A073404 A073405 A073406
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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